Deep, persistent problems are never solved by accident; they are solved only by people who are obsessed with them and set out to solve them directly.

The page of my notebook was filled with many messy integrals, but all of a sudden I saw emerge a formula for counting. I had begun to calculate a quantity on the assumption that the result was a real number, but found instead that, in certain units, all the possible answers would be integers. This meant that areas and volumes cannot take any value, but come in multiples of fixed units.

Some string theorists prefer to believe that string theory is too arcane to be understood by human beings, rather than consider the possibility that it might just be wrong.

But in spite of the obvious effectiveness of mathematics in physics, I have never heard of a good a prioriargument that the world must be organised to mathematical principles.

Simplicity and beauty are the signs not of truth but of a well-constructed approximate model of a limited domain of phenomena.

Those who do good science do so because they choose problems that are suited to them.

Science is not about what's true or what might be true, science is about what people with originally diverse viewpoints can be forced to believe by the weight of public evidence.